For astronomical objects, the time period can be calculated using:
T² = (4π²a³)/GM
where T is time in Earth years, a is distance in Astronomical units, M is solar mass (1 for the sun)
Thus,
T² = a³
a = ∛(29.46²)
a = 0.67 AU
1 AU = 1.496 × 10⁸ Km
0.67 * 1.496 × 10⁸ Km
= 1.43 × 10⁹ Km
First find the time it takes to hit the sand t
using s=1/2 g t^2
t^2= 8/9.8= 0.82 seconds
This means the sand was s = 8 * 0.82 = 6.5m away
The horizontal speed stays constant at 8 m/s
The vertical speed =.82 * 9.8 = 8.0 m/s
As the two velocities are equal the angle must be 45 degrees to the horizontal
